The baby is 1.5 months old.
She is currently being bottle fed.
At what age should we replace the bottle with a cup, and how should we go ahead introducing the change?
The American Academy of Pediatricians recommends stopping bottle useage at age 1. Many pediatricians recommend making the switch away from the bottle by 15 months. Others set the limit at 18 months. A few say the switch is not necessary until 2. The concerns with extended bottle feeding are:
While a few parents go directly from a bottle to a sturdy, open tumbler, most parents use a sippy cup or a straw cup as a transitional cup. The straw cup is considered superior for oral motor development. The choice is entirely up to you. Our pediatric dentist did recommend not using a sippy cup for too long as the sippy cup is not helpful for oral motor skills or teeth.
Usually a cup of water is introduced at mealtimes when solid foods are introduced. This cup is more for practice than for hydration. There are usually three methods of making the final transition for toddlers over 12 months of age.
Sites like the very pro-breastfeeding kellymom.com also provide alternatives to the bottle for infants under 1 year of age. For example they recommend cup feeding using a cup such as the Foley cup. This resource also talks about teaching a special needs child how to use a straw cup and gives you all sorts of resources on straw cup useage. So should you desire to move away from the bottle in the 4 to 6 month range, it is possible though not necessary.
Rather than an age, I'd watch for when she can manipulate a toy well with one hand. By 'well' I mean she can control its orientation and position with enough accuracy that water/milk won't spill everywhere. Once she can do that, just give her a small cup about 1/4 filled to start with; she should get the hang of it within a few weeks.
I believe that we started my son around 12 months old, though we could have done it sooner.